My letter to Mike and Steve
I consider Steve Jacobs and Mike Shackleford to be two of the foremost combinatorial analysts we have today in the field. I think Cacarulo is the third, but I don't have his e-mail address! Here is my letter. In the meantime, I'm going to check over at bjmath. There may be something there, as well.
Don
Steve,
How are you? Hope all is well. There's a fine point of BS discussion going on on bj21, and I thought I'd solicit some input from you.
For SD, H17, it appears, from Griffin, p. 173, and from Wong's appendixes, that splitting nines vs. ace is correct only when DAS is permitted. Apparently, the EV for splitting with das is -0.185+, while the EV for standing is -0.186. However, with no das, the EV for splitting drops to -0.193+, and standing is now the correct BS play.
Mike, your Appendix 9B indicates this clearly, but your SD H17 BS chart is wrong, because you give "P," as if pair-splitting were always correct, when you should be giving "S/P," which doesn't exist in your legend. This is a unique hand! Also, Mike, your top chart in 9b says "Hands Which May Be Split," when you mean "May Not." Have you done this with all of the double charts? You'd better check!
Back to Steve: Now, to make matters interesting, someone has hypothesized that maybe the -0.193 for no DAS is correct only when a single split is permitted, and that, when two or three splits are permitted, the EV improves to a point where it may be superior to standing, even with no DAS. Although I doubt this very, very much, I wonder if you would take a look, please. Note that Griffin does NOT recommend splitting for this play if no DAS. But, it's worth checking him, right Steve?! :-)
Thanks.
Regards,
Don